This paper presents a branch-and-cut method for two-stage stochastic mixed-integer programming (SMIP) problems with continuous first-stage variables. This method is derived based on disjunctive decomposition (D2) for SMIP, an approach in which disjunctive programming is used to derive valid inequalities for SMIP. The novelty of the proposed method derives from branching on the first-stage continuous domain while the branch-and- bound process is guided by the disjunction variables in the second-stage. Finite convergence of the algorithm for mixed-binary second-stage is established and a numerical example to illustrate the new method is given. Keywords: stochastic programming, disjunctive decomposition, branch-and-bound, branch-and-cut